Path planning using Harmonic Functions and Probabilistic Cell Decomposition

Potential-field approaches based on harmonic functions have good path planning properties, although the explicit knowledge of the robot’s Configuration Space is required. To overcome this drawback, a combination with a random sampling scheme is proposed. Harmonic functions are computed over a 2 d-tree decomposition of a d-dimensional Configuration Space that is obtained with a probabilistic cell decomposition (sampling and classification). Cell sampling is biased towards the more promising regions by using the harmonic function values. Cell classification is performed by evaluating a set of configurations of the cell obtained with a deterministic sampling sequence that provides a good uniform and incremental coverage of the cell. The proposed planning framework opens the use of harmonic functions to higher dimensional C-spaces.